Your "axioms" are far too complicated to be truly axiomatic.
A very obvious metaphysical axiom is that "something exists." It is unimaginable that that statement could be untrue.
A fundamental mathematical axiom might be " if X and Y have the same elements then X=Y"
I'll also put foward the following as undeniable, but only because the consequences of it being untrue make life meaningless. If life has no meaning then there's really no point in arguing. I might be a little off on a few of these, I'm open to a bit of debate but the fundamental idea is solid and undeniable.
"Knowledge (to some degree) is possible"
"Goodness exists"
"Moral actions are possible"
"Immoral actions are possible"